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Norm-Resolvent Convergence in Perforated Domains

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For several different types of boundary conditions (Dirichlet, Neumann and Robin), we prove norm-resolvent convergence in L2 for the Laplacian in an open domain perforated epsilon-periodically by spherical holes. The limit operator is of the form -Δ+m on the unperforated domain, where m is a positive constant. This is an improvement of previous results [Cioranescu & Murat. A Strange Term Coming From Nowhere, Progress in Nonlinear Differential Equations and Their Applications, 31, (1997)], [S. Kaizu. The Robin Problems on Domains with Many Tiny Holes. Proc. Japan Acad., 61, Ser. A (1985)], which show strong resolvent convergence. In particular, our result implies convergence of the spectrum of the operator for the perforated domain problem.

This talk is part of the Applied and Computational Analysis series.

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